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Proceedings of the American Mathematical Society

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All $ n$-uniform quasitranslation Hjelmslev planes are strongly $ n$-uniform


Author: David A. Drake
Journal: Proc. Amer. Math. Soc. 51 (1975), 494-498
MSC: Primary 50D35
DOI: https://doi.org/10.1090/S0002-9939-1975-0377685-7
MathSciNet review: 0377685
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Abstract | References | Similar Articles | Additional Information

Abstract: An affine $ H$-plane $ \mathcal{A}$ is called a quasitranslation $ H$-plane if it possesses a group of quasitranslations which is regular on the points of $ \mathcal{A}$. Let $ n$ be any positive integer. Then every $ n$-uniform quasitranslation $ H$-plane is strongly $ n$-uniform.


References [Enhancements On Off] (What's this?)

  • [1] B. Artmann, Desarguessche Hjelmslev-Ebenen $ n$-ter Stufe, Mitt. Math. Sem. Giessen 91 (1971), 1-19. MR 45 #4270. MR 0295202 (45:4270)
  • [2] D. A. Drake, On $ n$-uniform Hjelmslev planes, J. Combinatorial Theory 9 (1970), 267-288. MR 42 #3667. MR 0268770 (42:3667)
  • [3] -, The structure of $ n$-uniform translation Hjelmslev planes, Trans. Amer. Math. Soc. 175 (1973), 249-282. MR 46 #9853. MR 0310755 (46:9853)
  • [4] H. Lüneburg, Affine Hjelmslev-Ebenen mit transitiver Translationsgruppe, Math. Z. 79 (1962), 260-288. MR 25 #1479. MR 0138031 (25:1479)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0377685-7
Keywords: Hjelmslev plane, level $ n$, $ n$-uniform, strongly $ n$-uniform, translation ($ H$-plane), quasitranslation ($ H$-plane)
Article copyright: © Copyright 1975 American Mathematical Society

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